This application relates to characterizing a texture of an image.
Melanoma is the deadliest form of skin cancer and the number of reported cases is rising steeply every year. In state of the art diagnosis, the dermatologist uses a dermoscope which can be characterized as a handheld microscope. Recently image capture capability and digital processing systems have been added to the field of dermoscopy as described, for example, in Ashfaq A. Marghoob MD, Ralph P. Brown MD, and Alfred W Kopf MD MS, editors. Atlas of Dermoscopy. The Encyclopedia of Visual Medicine. Taylor & Francis, 2005. The biomedical image processing field is moving from just visualization to automatic parameter estimation and machine learning based automatic diagnosis systems such as Electro-Optical Sciences' MelaFind, D. Gutkowicz-Krusin, M. Elbaum, M. Greenebaum, A. Jacobs, and A. Bogdan. System and methods for the multispectral imaging and characterization of skin tissue, 2001. U.S. Pat. No. 6,081,612, and R. Bharat Rao, Jinbo Bi, Glenn Fung, Marcos Salganicoff, Nancy Obuchowski, and David Naidich. LungCad: a clinically approved, machine learning system for lung cancer detection. In KDD (Knowledge Discovery and Data Mining) '07: Proceedings of the 13th ACM SIGKDD international conference on Knowledge discovery and data mining, pages 1033-1037, New York, N.Y., USA, 2007. ACM. These systems use various texture parameter estimation methods applied to medical images obtained with a variety of detectors.
A relatively recent class of texture parameters (features or descriptors in machine learning jargon) was inspired by Fractal Geometry. It was introduced by B. B. Mandelbrot. The Fractal Geometry of Nature. Freeman, San Francisco, Calif., 1983. as a mathematical tool to deal with signals that did not fit the conventional framework where they could be approximated by a set of functions with a controlled degree of smoothness. It can describe natural phenomena such as the irregular shape of a mountain, stock market data or the appearance of a cloud. Medical data is a good example of signals with fractal characteristics. Sample applications of fractal analysis include cancer detection, for example, as described in Andrew J. Einstein, Hai-Shan Wu, and Joan Gil. Self-affinity and lacunarity of chromatin texture in benign and malignant breast epithelial cell nuclei. Phys. Rev. Lett., 80(2):397-400, January 1998, remote sensing, for example, introduced in W. Sun, G. Xu, and S. Liang. Fractal analysis of remotely sensed images: A review of methods and applications. International Journal of Remote Sensing, 27(22), November 2006, and others, for example, Wikipedia. Fractal—wikipedia, the free encyclopedia, 2007.
In signal processing, the Wavelet Transform is often described as a space-scale localized alternative to the Fourier Transform. Wavelet maxima extract the relevant information from the wavelet representation. The space-scale localization property makes wavelets and wavelet maxima a natural tool for the estimation of fractal parameters as described, for example, in Heinz-Otto Peitgen and Dietmar Saupe, editors. The Science of Fractal Images. Springer Verlag, 1988, and Laurent. Nottale. Fractal Space-Time and Microphysics: Towards a Theory of Scale Relativity. World Scientific, 1992, and S. Mallat. A theory for multiresolution signal decomposition: the wavelet representation. 11(7):674 -693, July 1989, and Stephane Mallat. A Wavelet Tour of Signal Processing. Academic Press, 1999.